Variational integrators for the dynamics of thermo-elastic solids with finite speed thermal waves

JOURNAL OF COMPUTATIONAL PHYSICS

卷:257

Article

Mata, Pablo^1,2  Lew, Adrian J.¹ 

[1] Stanford Univ, Dept Mech Engn, Stanford, CA 94305 USA

[2] Univ Austral Chile, Conicyt Reg CIEP R10C1003, CIEP, Ignacio Serrrano 509, Coyhaique, Chile

关键词: Variational integrators;    Geometric integration;    Symplectic methods;    Thermo-elasticity;   

DOI  :  10.1016/j.jcp.2013.09.030

来源: Elsevier

【 摘 要 】

This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the fact that the Green-Naghdi theory of type II for thermo-elastic solids has a Hamiltonian structure. Thus, standard techniques to construct variational integrators can be applied to finite element discretizations of the problem. The resulting discrete-in-time trajectories are then consistent with the laws of thermodynamics for these systems: for an isolated system, they exactly conserve the total entropy, and nearly exactly conserve the total energy over exponentially long periods of time. Moreover, linear and angular momenta are also exactly conserved whenever the exact system does. For definiteness, we construct an explicit second-order accurate algorithm for affine tetrahedral elements in two and three dimensions, and demonstrate its performance with numerical examples. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free